High power factor current limiter



1954 'r F. CARMICHAEL 2,665,406

HIGH-POWER FACTOR CURRENT LIMITER Filed April 1, 1946 3 Sheets-Sheet l I FIE- 117.

- amen tom K -Ej TFRHZER EFIEMIEHHEL 35 3:34? V Z Jan. 5, 1954 T F. CARMICHAEL. 2,665,406

HIGH-POWER FACTOR CURRENT LIMITER Filed April 1, 1946 3 Sheets-SheetZ FIEFYUL FILTE- T. FF'FYZER EHRM/EHFIEL Jan. 5, 1954 T F. CARMICHAEL 2,665,406 HIGH-POWER FACTOR CURRENT LIMITER Filed April 1, 1946 3 Sheets-Sheet 3 52 54 253 H F-sa 5s 3 A FIEFEL awe/whoa:

IFRHZER EHHM/EHHEL 3&3 GM 9 Patented Jan. 5, 1954 UNITED STATES PATENT OFFICE HIGH POWER'FACTOR CURRENT LIMITER Thomas-Frazer Carmichael, Plymouth, Mich. Application April 1, 1946, Serial No. 658,623" 6 Claims. (01.323-45) The present invention relates toballasts for gaseous discharge loads, and more particularly to ballasts for fluorescent lamps to maintain a high power factor load. This is a continuationin-part of my copending application Serial No. 400,136, filed June 2'7, 1941, for High Power Factor Current Limiter, now abandoned.

'I'he characteristics of fluorescent lamps are such that when connected to a well regulated voltage source, they will draw an excessive amount of current. In order to limit the amount of current drawn, there is ordinarily included in series with each lamp and its electric power source, a choke coil. However, due to its inductive nature, the choke coil and the lamp with which it is associated, form a low power factor load. Since for reasons well known in the art a high power factor load is desirable, the low power factor load obtained by employing a choke coil is raised to a high power factor load b connectin a capacitor across the conductors of the input power line. The provision of both a choke coil and a capacitor as an auxiliary, which in the trade are combined as a unit known as a ballast, not only increases the expense of fluorescent lighting units but also the ballast is somewhat bulky requiring a substantial amount of space. According to the present invention there is provided a fluorescent lamp high power factor ballast consisting solely of inductances on a core, which not only costs less to manufacture than the combination choke coil and capacitor high power factor ballast, but also takes up less space.

Briefly, this invention in its basic form consists of a core providing a magnetic circuit having disposed therein, two coils connected in series across the electric power source and the fluorescent lamp loadshunted across one of the coils on the core. The arrangement is such that the current drawn by the fluorescent lamp load is limited and at the same time the line power factor is not excessively lowered from the unity power factor of the lamp itself which is equivalentto a resistance.

An object of the invention is to provide a gaseous discharge lamp ballast for limiting the current drawn by the lamp without substantially decreasing the power factor thereof.

Another object of the invention is to provide for a fluorescent lamp a ballast for limiting the current drawn thereby without substantially lowering'the power factor thereof andwithout employing a capacitor.

Still another object of the invention. is to provide. for a fluorescent lamp, a ballast forlimit- 2 ing the current drawn thereby, in the form of a transformer with predetermined leakage inductances.

A still further object of the invention is to provide" a high power factor current limiting device for'gaseous discharge loads.

A still further object of the invention is to provide a fluorescentilamp ballast in the form of an autotr'ansformer having poor regulation.

AI still further object of the invention is to provide a fluorescent lamp ballast'in the form of an autotransformer having'regulation decreasing with load..

A still further object of the invention is to provide'a fluorescent lamp ballast which maintains a uniform lamp current throughout the current cycle thus operating the lamp at its most eflicient condition.

A still further object of the invention is to provide a ballast which minimizes changes in lamp current due to variations in line voltage.

A still further object of the invention is to provide a high filament current for preheating gaseous discharge lamp filaments for starting.

A still further object of the invention is to provide more leakage reactance than is practical in an ordinary autotransformer of nearly one to one turns ratio.

These and other objects will be apparent from the following specification when taken with the accompanying drawings, in which Fig. 1 is a diagram showing one form of unit according to the present invention,

Fig. 2 is asimplified wiring diagram of the unit disclosed in Fig; 1,

Fig. 3 is a form of the invention showing the use of a gap in: the iron core,

Fig. 4 is a" form of the'invention showing the meet magnetic shunts,

Fig. 5 discloses a form of the invention using three coils,

Fig. 6 is a simplified Wiring diagram of the unit disclosed in Fig. 5,

Fig. '7' is a wiring diagram for a form of the invention for operating two lamps,

Fig. 8 is a. wiring diagram for another form of 'the invention, for operating two lamps,

Fig. 9 is a wiring diagram for another form of the invention for operating two lamps,

Fig. 10 is a wiring diagram for another form of. the invention for operating more than one p.

Fig. 11 isawiring diagram for another. form of the invention for "operating more than one lamp,

Figs. 12 and 13 illustrate another form of the invention, and

Figs. 14, 15 and 16 are simplified circuits for the purpose of mathematically analyzing the invention.

Referring particularly to the drawings, reference character I indicates a conventional hot cathode fluorescent lamp lighted from a source 2 of alternating electrical current, ordinarily of about 118 volts, The source 2 isadapted to be connected to terminals 3 and 4 by a switch 5. The lamp I is provided at the opposite end thereof with thermionic eelctrodes or filaments 6 and I.

A series coil 8 is connected in series between the terminal 3 and one terminal of the filament 6, a conductor 9 providing a connection between the terminal 3 and one end of the series coil 8, and a conductor I providing a connection between the other end of the series coil 8 and the filament 6. A shunt coil II is shunted across the filaments 6 and I, a conductor I2 connecting one end of the shunt coil II to the conductor III, and a conductor I3 connecting the other end of the shunt coil II to a conductor I4. The conductor I4 connects one terminal of the filament I with the terminal 4.

The other terminals of the filaments 6 and 1 are connected by conductors I8 and I9 respectively to a starting switch 20, which may be a conventional glow relay, a delayed action magnetic or thermal switch, or a manually operated switch to preheat the filaments. In any case, however, the starting switch 20 is opened shortly after the main switch is closed to start the lamp I, as will be well understood by those skilled in the art.

The series coil 8 and the shunt'coil II are mounted on the leg 2| of a laminated iron core and are arranged in the circuit above described so that their directions of winding are continuous about the leg 2|. The core is made up of a stack 22 of E-shaped laminations.

In operation to start the lamp I, the switch 5 is closed, after first closing the starting switch 20, either automatically or manually. In a typical automatically operating starting switch 20, as soon as the switch 5 is opened to put out the lamp I, the starting switch 20 closes. Also in an atuomatic switch 20, after the switch 5 has been closed for starting the lamp, the starting switch 20 opens after a short period of time which is sufiicient to permit the filaments 6 and I to heat to incandescence. When the starting switch 20 is manually actuated, it is opened man- I ually after a short period of time following the closing of the switch 5. As the starting switch 20 is opened, a voltage surge causes the current from the source 2 to are across the filaments 6 and 1 providing an ultraviolet radiation which causes the lamp I to provide a light due to the fluorescent coating on the inside of the tube thereof.

The characteristics of the lamp I are such that without some device to limit the current which it draws from the source 2, the arcing across the filaments 6 and I increases the ionization of the gas within the lamp I, which causes the lam I to draw more current which in turn causes increased ionization within the lamp I. Accordingly, in order to prevent the lamp from drawing increased amounts of current to a point at which it will burn itself out, some current limiting device must be employed. Some drop in voltage is also necessary since more voltage is required to be observed from Fig. 2 constituting a simplified wiring diagram of the circuit in Fig. 1, the series coil 8 and shunt coil II constitute a step-down autotransformer with internal leakage reactance to reduce the output voltage with increasing load current. This is necessary in order to provide regulation for the lamp I or other discharge device with which the invention is used, to prevent the discharge device from drawing excessive current due to its negative resistance characteristics. The ballast steps down the line voltage as much by its autotransformer action, as will still provide the voltage required to start the lamp, and utilizes only sufficient leakage reactance voltage drop to prevent the lamp from drawing excessive current due to its negative resistance characteristics. B this means the ballast maintains a higher power factor than the ordinary series inductance ballast which must have a large reactance Voltage drop to lower the voltage from the line voltage to the lamp operating voltage and hence has a poor power factor.

In the design of the unit according to the present invention it is desirable that the voltage between the filaments 6 and I be high enough to start the lamp on open output circuit, that is, after the filaments are preheated and the starting switch 20 opens. For instance, for a typical 20 watt fluorescent-lamp the operating voltage is about 60 volts, but an open output circuit voltage of more than volts is necessary for start- Any practical ballast will have some resistance. The equivalent resistances will include copper losses and iron losses. These reduce the power efiiciency of the ballast and as such are undesirable even though by adding resistance load they do not improve the line power factor. Another eifect of the resistance of a ballast is to provide voltage drop under load in addition to any purely inductive voltage drops. For some fluorescent lamps it is even possible to use only a series resistor as a ballast and obtain unity power factor, but with very poor efficiency. On direct current lines this must, however, be done.

In the design of ballast according to this invention, the losses may be kept low by using large wire for the coils and large cores of low loss material operated at low flux density. The actual designs follow transformer practice except that the coils are arranged for predeterminedly large leakage reactance. This leakage reactance may also be increased by use of air gaps or by saturable core parts, of which magnetic shunts are examples. To achieve the desired results according to the present invention, the leakage reactance should be increased to such a value that it will be small enough not to result in a low power factor, but yet large enough and substantially constant to decreasing in value, when taken with the resistance of the ballast, to drop the ballast output voltage more with increasinggload current ial-mnthe negative resistance f charaoteristlcrload voltageidrops with equal-valuesof-increasing current. Thus; if "the leakage reactance istoo small the :power factor will be high,- but" amine-resistance 01' the. negative resistance characteristicload-"decreases and thus tends to' draw mora -current, the-'-bailast 1 will not limit current and th'e Y load' -will" draw increasing amounts of current'until it b'urns out.

Because of the'good regulation 1 ofthe ballast inthis invention, it furnishes a high filament current for quick starting.

A suitable design'accord-ing-to the present 'lnvention would; for a-typical zowattlamp, be constructed as foll'ows' z On ashell type core h'aving ,4 wide'windows extending along a /5" widecenter leg of' a: A." stack of transformer lam-ination's' there would betwo cells. The coils would be 1600 turns =ol? #38-A1 W. G. and 4400 turns of #34 A; W. G; enameled copper wire. They would be lndivldu'ally wound as pies and spaced as far apart on the core legas 'possible; By this meansa'largelakage reactanee isobtai'ned. Such a ballast'connected as in Fig. 1 to a 1l8 volt 60'cycleline and to a 20 watt fluorescent -lamp starts with a standard starter. It has an open circuit output voltagecf 90 volts; In operation, this ballast supplies :242 ampere at 63-volts to the la. 'pwhile drawing 0.195-am pere' and -22"watts from the line. Its line power factor is watts/volts amperesor 22/118 -0.195 or" 01957. Acommercial seriesreactor ballast for this same lamp has a line power factor of less than 065 without a condenser.

Theoperation of the ballastdescribed in this invention has been theoretically described as being similar to an autotran'sformer having" resistance and large leakage reactance; This has been checked by measuring the'constants of the 20 watt ballast described and calculating its performance theoretically; Theequivalent circuit of any transformer is-an ideal -(lossless) transformer with series input and output inductances (see any standard'text). The input maybe shunted by an impedance representing the magnetizing current. The magnetizing current as measured 'at no load on the 20 watt ballast was less-than 0.005-ampere-and hencenegli'gible. All

equivalent circuit for the watt ballast then is an ideal transformer of 118/90 ratioand with 98.5 ohms resistance and 122" ohms reactance is 0.245 amperewhijch compares with the 0242 actually measured. The powerfactor ofthe equivalent circuitis .930 compared to the .957 of the actual circuit. The calculated watts are 20:6 compared to ameasured:22 watts and the calculated current of:0'-.-18 -7 amper -comparesrwith the measured value of 0.195 ampere; These were 98.5 ohms resistvalues: all are within the errors of. the. actual.

readings.

Fig: 3 shows-another form of this invention wherein the-'centerleg'ZE ofthe core'21 is made with an air'gap 28 tending to decrease the mutual fluxin the coils 'rand hence :toincrease the proportion of leakage flux and. thusflleakage reactance. The circuit'is the same as that oi! Figs. land 2;

Fig. 4 shows another form of-thisinventi'on wherein thel'eakage flux between the coils 8 and H is increased by inserting magnetic shunts 30 and-3i between them; For high-power factor operation'these shunts should be of a design or material, such: as a nickel-iron alloy, that'saturateslat alower-field'strength than the balance of the core material which usually will he silicon steel; Theseshuntsv will then tend to saturate when load current is'drawn' from the ballast. Their-saturation in the vicinity of'full load will limit the leakage flux and reduce the leakage reactance thus improving the power factor and regulation of the ballast. However, the leakage reactance of the design is still greater than it would be without the shunts 30 and 3 l,- to'provide the desired operating voltage drop. By this method: a higher starting voltage can be obtained without sacrifice of power factor.

Fig. 5 shows the form of the invention for discharge devices which require'starting voltages near or above line'voltage. This consists of two coils 32 and'33' in series across the lines and a'third' coil 34 connected to the junction of the first two and which steps the voltage up to, near or above line voltage while providing large leakage reactance.

Fig.- fi' shows the circuit of this form of'the invention. In order to increase the leakage reactan'ce' of the'formof the invention disclosed in Figs. 5 and 6-wherein'an additional voltage coil saturable core parts asfor example magnetic shunts may be employed, but it has been found most satisfactory to merely space any two ofthe coils. However, any combination'of gaps, shunts or coil spacing may be used. As'shown, coils 32 and 33 arespaced, but if desired, the spacing could be between the coils 32 and 34;' However, it is to be understood that a-slight spacing of each of the coils might equally well be used to obtain the reactance desired.

shunt coil equivalent is the combination of the coils 39 and 40 and the series coil equivalent is the coil 4|. 'I'he 'equivalent of the voltage= coil 34'of'Figs. Sand 6' is the voltage of-a20 watt fluorescent lamp, the operating volt age is about 63 Volts as hereinabove explained.

A voltage 'coil is not required when a .120 volt line is used as a source of power for this lamp.

In some applications of the inventionitmay be desirable to omit the center coil 40 of Fig. 1. Such an arrangement is shown in Fig. 8. The operation or the arrangement of Fig. 8 is identical to that shown in Fig. 7 except that the shunt coil for the lamp 3'! consists of only the coil 39 and the shunt coil for the lamp 38 consists of only the coil 4 I.

The arrangement of Fig. '7, since it employs voltage coils 42 and 43, is, as explained above, for use with lamps operating at a voltage at or above line voltage. If the lamps may be operated at a voltage less than line voltage, the voltage coil 42 and 43 may be omitted as disclosed in Fig.9.

Still another form of the invention is disclosed in Fig. '10 which is a variation of the circuits disclosed in Figs. 8 and 6 for the operation of two lamps 45 and 46. In this form of the invention each lamp has a common shunt coil 41 and series coil 48, but separate voltage coils, the lamp 45 having a voltage coil :39 and the lamp 49 having a voltage coil 59.

Another form of the invention is disclosed in Fig; 11 which employs the same components as disclosed in Fig. 7, but the connections are such as'to provide less output voltage. As explained above, in Fig. 7 the shunt coils for the lamp 3'! consist of the two coils 39 and 49 and the series coil consists of the coil 4|. In Fig. 11, the shunt coil for the lamp 3! consists of the single coil 39 and the series coil consists of the two coils 40 and 4!. Thus the step-down turns ratio of the transformer is more for the Fig. 'I arrangement than it is for the Fig. 11 arrangement. Likewise, the connections for the lamp 38 are such that its shunt coil consists of the ingle coil 4| and its series-coil consists of the two coils 39 and 49. v

In each of the forms of the invention, Figs. through 11, the desired leakage reactance as explained forthe arrangement of Fig.5 could be obtained by the use of core gaps, saturable core parts as for examples magnetic shunts, or by spacing of coils, but preferably it is obtained by the appropriate spacing of the respective coils. Thus, for a two lamp arrangement there should be the equivalent of spacing between at least two of the coils for each lamp so as to provide leakage reactance components effective for each lamp.

A specific example of a ballast constructed according to the teachings of Fig. 8 is one having the coils 42, 43, 39 and M wound on the center leg of a, core as shown in Fig. 5, with the coils 42 and 43 physically located between the coils 39 and M. The stack comprising the core is 1 /2 inches high. The center leg is 1" wide and all outside legs are wide. Coils 39 and 4| are each 545 turns of Number 22 enameled copper wire and coils 42 and 43 are each 600 turns of Number 23 enameled copper wire. Such a ballast-operates two 100 watt fluorescent lamps at a power factor of .85 with a 45 watt loss. It will be apparent that the step-down autotransformer turns ratio for each lamp is 545-1-545 or 1090 to 545, and that the step-up turns ratio from line voltage is It will be understood that the voltage under load drops due to the leakage reactance of the transformer.

Another specific example of the invention is as follows and is applied to the form of the invention shown inFig. 8-. 1 The core is the same as is shown in Fig. 5 and consists of a stack of laminations 1" deep with a 1" Wide center leg and one-half inch wide other legs and ends. The windows are seven-sixteenthswide. All turns are on the center leg. The coils 42 and 43 are 705 turns of Number 23 copper wire and the coils 39 and 41 are 545 turns of Number 23 copper wire. Each lamp is watts. A power factor of .80 is obtained and an open circuit voltage of volts from a 118 volt line.

Still another form of the invention is illustrated in Figs. 12 and 1 3. In thi form of the invention there is an irregular core structure, the irregularity of which provides a leakage reactance obtained in other forms of the invention by core gaps, magnetic shunts, or by spacing of the coils. The specific embodiment disclosed in Figs. 12 and 13 is designed for use with two 40 watt fluorescent lamps.

The small core portion 50 consists of a stack of laminations /2 inch wide and /2 inch deep which is mortised in the larger core portion 5! which is A" wide at the end, 1 inch Wide at the legs and 1 inches deep. The coils 52 and 53 consist of 1800 turns each of #26 copper wire, the coils 5G and 55 consist of 350 turns each of #29 copper wire, and the coils 5G and-5i consist of 880 turns each of #28 copper wire.

The operating statistics for the ballast of Figs. 12 and 13 are as follows: Power factor .84, and open circuit voltage 176 when connected to a 118 volt line. The difierence between a theoretical turns ratio of turns across the lamp to turns across the-line, times the line voltage, which is approximately 188 volts, and the actual open circuit voltage of 176 volts, is accounted for by losses.

The voltage coils in each of the forms of the invention'where the operating voltage of the load is about or above line voltage should have a turns ratio with its associated series coil to provide the desired operating voltage. This will be clear when it is observed that the basic circuit in each case, without a voltage coil, is a step-down autotransformer. Thus, with a voltage coil there is provided what might be termed a step-downstep-uptransformer, wherein the step-up turns ratio is the ratio of turns across the lamp to turns across the line.

Summarizing the invention, it will be clear that in order to obtain a limiting of the current of a negative resistance characteristic load, there is used a step-down autotransiormer either with or without a voltage coil for increasing the voltage output. The transformer must'have a leakage reactancewhich is large enough to prevent the load from running away, that is, drawing increasingly large amounts of current until it burns up, and is yet small enough to result in a high power factor. To design a ballast according to the present invention, the turns ratio of the autotransformer should be calculated so as to provide a starting voltage equal to that required by the load. Enough leakage reactance then should be introduced until the output voltage at rated load current drops to the rated load voltage. Due to the copper and iron losses in the ballast, it will have an equivalent resistance. This will cause some drop in output voltage with load. It will be understood that the resistance losses in the ballast are power losses and, therefore, should be minimized.

imam

The introduction of leakage reactance andrresistance to the theoretical ballast using the above turns ratio will result ina changedno load'starting voltage. Accordingly, the turns ratio should be revised to.compensate'for the change-.dueto the added leakage reactance and resistance. The resultant ballast may then have to be revised-to add or subtract leakage'reactance in order to prevent the load from running away. It :may still be necessary after-this pointJhas been reached to revise the turns ratio. When as many :ad'justments have been made as necessary, the resultant ballast will vhave a no-load voltage equal to thatrequired to start the load and;will at:v the same time have sufficientseries impedance'to prevent theload from running away, thatiathe output voltage at rated'load current willequal the rated load voltage. As pointed out hereinabove, the leakage reactance may be obtained by spacing the coils, by introducing saturable core parts as for examples magnetic shunts in the core, or by gapping the core. The resistance may be in any of the coils and is adjusted by varying the size of the wire. Resistance could be introduced in series with the load or line, but as this would introduce a power loss, it should not be used. Leakage reactance provided by saturable magnetic shunts decreases with increasing load cur-' rents. Leakage reactance'provided byspacing of coils or by gapping the core is substantially constant with increasing load current.

The operation of the invention as far'as control of power factor'is concerned will be clear from an understanding that a voltage drop provided by a leakage reactance is inductive and thus causes a current in the output of the ballast to lag the voltage. Thus the greater the leakage reactance, the greater the current lag and thus the lower the power factor. For this reason a leakagereactance which increases with load current is not desirable. The operation of the-invention as far as current limiting is concerned is that the leakage reactance voltage drop limits the flow of current in the ballast and thus in the" load.

An analysis of the" present invention with the common series reactor ballast and :other circuits will probably make the novelty of the invention clear.

Fig. 14 is admittedly a simplified circuit since the coils are necessarily iron cored and have copper ohmic and eddy current losses" and the iron has hysteresis and eddy current losses. These losses, however, can be represented accurately by equivalent series resistances in the coils. The saturation of" the iron would also be a factor, but if the inductances of the coils were taken at their rated of the saturation would be to increase the hysteresis series coil resistance.

The lamp can be considered a pure resistance, but not a linear one. That is, its resistance will change with current. However, if the principle can be demonstrated by analysis for any of several fixed resistances, it should apply to one varying in that range.

Therefore, for the sake of simplicity, this first analysis will be made by assuming ideal (lossless) coils and a fixed (linear) resistance. These recurrents, the major effectsults agree with actual measurements hence justifying this simplification.

The circuit analysis which follows is carried out in general terms thus permitting the later substitution of anypa'rticular component values.

The circuit of Fig. 15 represents the simplified circuit to beanalysed.

The basic circuit equations for the currents and the mesh voltages 'are given by Kirchofis laws. These are vector equations:

For any given components L, L", .M, Rand voltage E alternating at w, only three variables are present. They are I, I", and I. Hence the three variables can'be found by solution of these three equations.

A solution for I follows:

Equation (1) multiplying by denominators E(RjwM+jwM+jwL) Equation (6) is therefore the general solution for I in terms of E, R, w, L, L", and M.

Since the power factor (the cosine of PS angle) is not readily apparent from (6) we will insert typical values of E, R, w, L, L", and M and calculate it. We will then also calculate the power factor for a simple series inductive ballast to give the same lamp current for the same E, R, and w.

Assume: E=l18 volts 60 cycle A. 0.

Also assume R=288 ohms, L=6 henries, L"=35 henries and M =13.6 henries. (Approximate values measured on an actual circuit.)

Therefore these typical components will theoretically run a 19.9 watt resistance load at 75.7 volts while maintaining a .90 power factor.

From (2) we see that if noload (R) is connected then I" must equal I and the starting voltage for the lamp will be j Hence the voltage drops from 84.1 to 75.7 when the load is applied and therefore this device has some load current regulation which is 12 necessary to limit the current to a fluorescent lamp.

Obviously, an autotransformer could be used to supply 75.7 volts from the 118 volt line but the autotransformer would not limit the load current nor would it provide a higher starting voltage.

A simple series reactor could be used on the 84.1 volt output line of an autotransformer to reduce the voltage to 75.7 for the lamp, limit the current and provide 84.1 starting volts. The power factor of such a unit would be 75.7/841 or .90. Therefore, this method would be equivalent in action to the circuit analysed but the separate reactor required for it would add cost.

A simple series reactor ballast as commonly used would for the same lamp conditions give a power factor of only 75.7/118 or .641. V

A series resistor could also be used and would give a 1.00 power factor, but with too much power loss to be economical.

Therefore the less regulation necessary to limit the lamp current, the smaller the ratio of load to no-load voltage will be. This ratio is equivalent to the power factor hence with less regulation the power factor will be much improved.

The foregoing analysis was derived for lossless coils to show that the operation of this device did not depend upon capacity or resistance for high power factor operation.

In that analysis it was stated that all coil losses were equivalent to resistances in series with these coils. The following analysis derives the basic equations taking into account the practical case with series coil resistances. By substituting typical resistance values, their effect on power factor is shown. Also included is a definition of limits of useful design.

Fig. 16 shows the equivalent circuit with coil resistance r in series with coil L and coil resistance r" in series with coil L". Other conditions are the same as before.

From Equation (6) above in the original analysis we had: V

Sincewe are effect substituting a coil and resistance for an ideal lossless coil we may write: :iwL (ideal) =r+iwL (practical) substituting the practical cases for the ideal in equation (6),

13 1.4 Multiplying terms with denominators by hotlc'athode' lamps operatingfrom120 volt lines, it is understood that the invention can be used l. to advantage on other gaseous discharge devices 7 or electrical loads having negative resistance and since 732-1 5 characteristics.

E(R+r+jwL") R(r+ +jw(L+2M+ L)+r1"+ jwL+ 1j +w Also substituting the practical case for the ideal Having thus described my invention, what Idein equation (4) above we obtain: sire to secure by Letters Patent and claim is:

l. A ballast for supplying an alternating our- IwL rent voltage to a load having negative resistance characteristics, comprising a plurality of mag- USing the same inductances, voltage, frequency netically coupled coils connected in series and and quival t lam resi ta c as n th id a constituting a primary winding, a magnetic core p E:118 Volts 60 cycle (1112377), on which said coils are arranged so as to have R=238 Ohms, 11:6 henries, hem'ies and 0 leakage flux between them, the coils being adapt- L"= h r eS nd using yp Values of ed for connection across an alternating current measured Coil resistances of T=120 Ohms and source in such manner that their direction of Ohmswinding is continuous around the core, and means -2ss 975 +j377 X 68.2) 10250 +j1580000+j1930000 142000085410) 281000+j7400000+10250+j1580000+j19300003550000 135+j1580 1581/85.l 35 adapted tcli gomect said loag1 between one and of =fi= sai p ura 1 y o coi s and e junc ion be ween 3259+J10910 104mm two of them, the coil or coils across which the Q load is connectable constituting a secondary '9 cos winding, coils of said primary winding having resubs l u n 1 for I In equation (8) 40 sistance and being spaced to produce leakage reactance and resistance of predetermined charac- I iig teristics in said ballast, said leakage reactance and resistance having a constant to decreasing 1459 j3565 3930/6820 1913 55 value with increases in the secondary current, W W said leakage reactance and resistance also being sufliciently large to decrease the ballast output The equivalent lamp v01tage=I'R= 191) 238:55 voltage with increasing secondary current a sufvolts and the lamp watts=I R=.191 283=10,5 ficient amount to limit said secondary current. watts, 2. The combination according to claim 1, fur- Comparison of the results with and without coil ther pro ded W a air p in a d re f resistance shows that the effect of the resistp d c ng said p de e n d l aka e reactanceance is: 3. The combination according to claim 1, there (1) To im rove the power factor from .90 to being wo ma n t c ly coupled coils c n t n .93 said primary winding, said core being further pro- (2) To reduce the efiiciency due to the coil Vided h an air ap f p du g said p losses termined leakage reactance.

(3) To reduce the current to the equivalent e co bi t o accord to c a m 1, furlamp resistance from .263 to .191 ampere and the ther provided with a saturable magnetic shunt line current from .190 to .152 ampere while refor producing said predetermined leakage reducing the lamp power from 19.9 to 10.5 watts. actance.

The improvement in power factor is obtained 5. The combination according to claim 1, said by unduly decreasing the efiiciency. Therefore, primary Winding constituting two coils, one of minimum coil losses are desirable. said coils constituting said secondary Winding.

While the foregoing invention has been de- 6. The combination according to claim 1, said scribed as applied particularly to fluorescent or primary winding constituting two coils, a third 0011 having one end connected to the junction of said first two coils, said load connecting means serving to connect said load between the other end of said third coil and the side of said primary winding farthest in potential from said other end of the third coil.

THOMAS FRAZER CARMICHAEL.

References Cited in the file of this patent UNITED STATES PATENTS Number Name Date 1,362,492 Kierstead Dec. 14, 1920 1,798,057 Bedell Mar. 24, 1931 1,950,394 Boucher Mar. 13, 1934 2,011,335 Friedman Aug. 13, 1935 2,114,535 Kirsten Apr. 19, 1938 Number Number 15 594,626

' Name Date Breer May 10, 1938 Boucher Feb. 13, 1940 Miner Apr. 2, 1940 Lord Aug. 19, 1941 Stocker Nov. 25, 1941 Fries Dec. 15, 1942 Haines Jan. 26, 1943 Lord Feb. 9, 1943 Owen June 22, 1943 Rypinski May 30, 1944 FOREIGN PATENTS Country Date Great Britain Nov. 14, 1947 

